That's who I was going to recommend. Ficciones is the place to begin. Also, I'd say Raymond Carver.

And in response to the comments about Lovecraft. I can agree that his writing may seem a bit awkward at times but he should be considered in context. Before HPL, there was little on the horror market to compare. Robert W. Chambers and Arthur Machen were the closest thing to that sort of writing. Well, Poe, also, of course. Lovecraft wrote for the pulps and the literary bar was not very high at the time. So, in context, he wrote some amazing things (Also, he's a young man's writer. I say "young man" intentionally because--at that time--I don't think the average woman was drawn to that sort of thing). Two other things to consider: 1) Lovecraft considered himself a 17th century aesthete and purposefully wrote in an archaic manner and, 2) at his best, he was a master of creating atmosphere.Folks like S. King have nothing on him.

Someone already mentioned Kurt Vonnegut's Welcome to the Monkey House collection, and I'll give another vote for it.

Nabokov wrote tons of short stories, all quite wonderful. And wonderfully depressing.

Tolstoy's The Death of Ivan Ilych and other stories is pretty good.

You also can't go wrong with Flannery O'Connor's A Good Man is Hard to Find. Southern Gothic at its best.

Margaret Atwood's Moral Disorder and other stories is great, too.

There's a certain amount of freedom involved in cycling: you're self-propelled and decide exactly where to go. If you see something that catches your eye to the left, you can veer off there, which isn't so easy in a car, and you can't cover as much ground walking.

James Tiptree Jr. If you like feminist science fiction, including arguably the first work of cyberpunk (even though The Girl a Who Was Plugged In predates the genre), then get Her Smoke Rose Up Forever. If Iain Banks never read Alice Sheldon, then I'd be a bit surprised.

This is a collection of 10 short speculative fiction stories, most taking part in near-future dystopias which some people might find disturbing or depressing, but I highly recommend it. Some stories are weaker then others, but most of them are great.